TP, AP, and MP From a Schedule: Find the Three Stages

Imagine a workshop with one beautiful old loom.

At first, it has too few shuttles moving through it. Add another shuttle and the loom becomes much more useful. Add a few more, and they work together in a smooth rhythm. The cloth grows rapidly.

But the loom itself has not become larger.

Eventually, each extra shuttle has less room to move. The cloth still grows, but by smaller additions. Add far too many shuttles and the threads begin to tangle. More input now produces less cloth.

That single journey explains total product, average product, marginal product, and the three stages of production.

The difficulty is rarely the idea itself. Most mistakes happen while reading a schedule. Students divide where they should subtract, confuse a falling marginal product with a falling total product, or place a stage boundary at the wrong turning point.

This guide will help you calculate every column, understand what each number is saying, and locate the three stages without guessing.

The Whole Topic in One Minute

Suppose labour is the variable input and all other inputs remain fixed.

TP = Total output produced

AP = TP / Units of labour

MP = Change in TP / Change in labour

When labour rises one unit at a time:

MP of the nth worker = TP with n workers - TP with (n - 1) workers

The quickest relationship map is:

What happens in the schedule?	What it tells you
TP rises by larger additions	MP is rising
TP rises by smaller additions	MP is positive but falling
TP is unchanged	MP is zero
TP falls	MP is negative
MP is greater than AP	AP rises
MP equals AP	AP is at its maximum in a smooth curve
MP is less than AP	AP falls

The three stage boundaries are found like this:

1. Stage I ends where AP is maximum and MP meets AP.
2. Stage II ends where TP is maximum and MP becomes zero.
3. Stage III begins when MP becomes negative and TP starts falling.

Keep these two boundaries separate. Maximum MP and maximum AP are not the same turning point.

First Fix the Setting: One Input Changes, the Others Stay Fixed

TP, AP, and MP schedules usually describe production in the short run.

In the short run, at least one factor is fixed. A farm may have a fixed area of land but can employ different numbers of workers. A bakery may have the same oven but can change the number of people working around it. A delivery centre may have fixed floor space but can add packers for a busy week.

We normally use labour as the variable factor because it makes the table easy to read. The logic works in the same way for any variable input.

The simplified production relationship is:

Output = f(variable input, fixed inputs)

If labour changes while capital is fixed, we can write:

Q = f(L), with capital held constant

This condition matters. If the number of workers and the number of machines both change, the schedule is no longer showing the same short-run movement along one product curve.

Total Product: The Output Collected So Far

Total product, or TP, is the total output produced by all units of the variable factor at a particular level of employment.

If four workers together make 64 baskets in a day, the total product of four workers is 64 baskets.

TP is not the contribution of the fourth worker alone. It is the output of the entire group of four workers with the fixed inputs available to them.

Think of TP as the complete length of cloth woven so far.

Average Product: Output Per Unit of the Variable Factor

Average product, or AP, is total product per unit of the variable factor.

AP = TP / L

If five workers produce 84 units:

AP = 84 / 5 = 16.8 units per worker

AP describes the average contribution, not the latest contribution.

At zero labour, AP is not zero. It is undefined because division by zero is not possible. Write a dash in that row unless the question gives some other instruction.

Marginal Product: The Addition Made by the Latest Unit

Marginal product, or MP, is the change in total product caused by a change in the variable input, while other inputs remain fixed.

MP = Change in TP / Change in L

If labour increases from four workers to five workers and TP rises from 56 to 75:

MP of the fifth worker = (75 - 56) / (5 - 4)
                         = 19 / 1
                         = 19 units

The fifth worker’s MP is 19. The AP of all five workers is 15. These numbers answer different questions, so they do not need to be equal.

A Complete TP, AP, and MP Schedule

Let us follow a small workshop that has fixed equipment and changes only the number of workers.

Workers (L)	Total Product (TP)	Marginal Product (MP)	Average Product (AP)	Stage
0	0	-	-	Starting point
1	8	8	8.00	I
2	20	12	10.00	I
3	36	16	12.00	I
4	56	20	14.00	I
5	75	19	15.00	I ends near here
6	89	14	14.83	II
7	98	9	14.00	II
8	102	4	12.75	II
9	102	0	11.33	II ends here
10	97	-5	9.70	III

This table is deliberately rich enough to show every important movement.

Calculate one AP value

At seven workers:

AP = TP / L
   = 98 / 7
   = 14 units

Calculate one positive MP value

For the seventh worker:

MP = TP at 7 workers - TP at 6 workers
   = 98 - 89
   = 9 units

Calculate zero MP

For the ninth worker:

MP = 102 - 102
   = 0

The ninth worker adds no output. TP remains at its maximum of 102.

Calculate negative MP

For the tenth worker:

MP = 97 - 102
   = -5

The tenth worker reduces total output by 5 units. That negative sign is meaningful. It shows overcrowding or interference, not a calculation to be corrected.

Read the TP Column Before Looking at Any Curve

The TP column alone reveals the sign of MP.

From 0 to 4 workers, TP rises by 8, 12, 16, and 20. The additions are getting larger, so MP rises.

From 4 to 8 workers, TP still rises, but the additions shrink from 19 to 14 to 9 to 4. MP is falling, but it remains positive.

From 8 to 9 workers, TP does not change. MP is zero.

From 9 to 10 workers, TP falls from 102 to 97. MP is negative.

This distinction is one of the most important ideas in the chapter.

Think of climbing a hill. Your height can keep increasing even after your speed begins to fall. You stop gaining height only when your upward speed becomes zero. If your vertical movement becomes negative, you begin to descend.

TP behaves like height. MP behaves like the rate at which height changes.

The AP and MP Relationship: The New Number Pulls the Average

You already know this relationship from ordinary averages.

Suppose your average score after four tests is 70.

• If the fifth score is 80, the average rises.
• If the fifth score is 70, the average stays at 70.
• If the fifth score is 60, the average falls.

MP plays the role of the latest score. AP is the existing average.

Therefore:

If MP > AP, AP rises.
If MP = AP, AP is stationary and reaches its maximum in the usual smooth curve.
If MP < AP, AP falls.

Check the workshop schedule.

At four workers, MP is 20 while AP is 14. The latest worker contributes more than the group average, so AP rises.

At six workers, MP is 14 while AP is 14.83. The latest worker contributes less than the group average, so AP falls.

In this table, MP moves from above AP to below AP between the fifth and sixth worker. The highest observed AP is therefore 15 at five workers.

Why MP may not exactly equal AP in a discrete table

In a smooth diagram, the MP curve cuts the AP curve at AP’s maximum point.

A table gives separate whole-number observations. The exact meeting point may lie between two rows. In that case, do not force equality by changing a value. Find where MP crosses from above AP to below AP and identify the highest listed AP.

This is why a schedule may show:

At L = 5, MP > AP
At L = 6, MP < AP

The crossover lies between those two input levels.

Three Turning Points That Students Often Mix Up

The full product story has three different turning points.

Turning point	What happens	What it means
MP reaches its maximum	TP changes from rising at an increasing rate to rising at a decreasing rate	Diminishing marginal returns begin after this point
AP reaches its maximum and MP meets AP	MP crosses AP from above	Stage I ends and Stage II begins
TP reaches its maximum and MP becomes zero	Another unit adds no output	Stage II ends and Stage III begins

The maximum point of MP is not the boundary between Stage I and Stage II.

In our schedule, MP reaches its maximum of 20 at the fourth worker. It then falls to 19 for the fifth worker. Yet AP still rises from 14 to 15 because MP remains above AP.

So diminishing marginal returns have begun, but Stage I has not quite ended.

Stage I: AP Rises and the Fixed Factor Is Underused

Stage I begins with the first unit of the variable factor and ends at maximum AP.

Its clearest identifying feature is:

AP is rising.

During this stage:

• TP rises
• AP rises
• MP is generally above AP after their starting equality
• MP may first rise and then fall
• the fixed factor is being used more effectively as variable input is added

In the workshop schedule, Stage I extends through the fifth worker, where the listed AP is highest at 15. The exact MP and AP crossover lies between five and six workers.

Why would a producer normally continue beyond the early part of Stage I? Because output per worker is still improving. The fixed equipment remains relatively underused, and an additional worker can raise the average productivity of labour.

Stage II: TP Rises at a Diminishing Rate and MP Stays Positive

Stage II begins after AP reaches its maximum and ends when TP reaches its maximum.

Its identifying pattern is:

AP falls, MP falls, but MP remains positive until the right boundary.

During this stage:

• TP continues to rise
• TP rises by smaller additions
• AP declines
• MP is positive but below AP
• MP reaches zero at the stage’s right boundary

In our schedule, Stage II runs from the sixth worker to the ninth worker. TP rises from 89 to 102, although each extra worker adds less output. At the ninth worker, MP is zero and TP is at its maximum.

This is called the economically relevant stage because neither factor is being used in an obviously wasteful way. Stage I leaves the fixed factor underused. Stage III uses so much variable input that total output falls.

However, Stage II is a range, not one automatic profit-maximising point. To choose an exact employment level inside Stage II, a producer would also need information about the value of output and the cost of the variable input.

Stage III: TP Falls and MP Is Negative

Stage III begins after TP reaches its maximum.

Its unmistakable sign is:

MP < 0

During this stage:

• TP falls
• MP is negative
• AP usually remains positive but continues to fall
• extra units of the variable factor obstruct production

In the schedule, the tenth worker has MP of -5. TP falls from 102 to 97.

Notice that AP is still positive at 9.7. A positive AP does not prove that an extra worker is useful. AP describes the average output of all ten workers. MP reveals that the tenth worker reduces the group’s output.

No rational producer would deliberately remain in Stage III if the extra variable input can be removed, because using less input would produce more output.

The Fastest Stage-Finding Method

When a question gives a complete TP, AP, and MP schedule, use this order.

Step 1: Find maximum AP

This marks the end of Stage I. In a smooth curve, MP equals AP here. In a discrete table, look for the MP crossover around the highest AP.

Step 2: Find maximum TP

This marks the end of Stage II. MP is zero at this boundary.

Step 3: Find the first negative MP

This is the beginning of Stage III. TP must now be falling.

For our schedule:

Maximum AP = 15 at L = 5
Maximum TP = 102 at L = 8 and L = 9
MP = 0 for the ninth worker
MP becomes negative for the tenth worker

Therefore:

Stage I: up to 5 workers
Stage II: after 5 workers through 9 workers
Stage III: beyond 9 workers

How to Draw the TP, AP, and MP Curves From a Schedule

The curves are not three unrelated drawings. They show the same table from different viewpoints.

Draw the TP curve

1. Put units of labour on the horizontal axis.
2. Put total product on the vertical axis.
3. Plot each pair, such as (1, 8), (2, 20), and (3, 36).
4. Join the points with a smooth curve if the question expects the usual theoretical shape.

The TP curve first becomes steeper because MP rises. It then becomes flatter because MP falls but remains positive. It is horizontal at maximum TP when MP is zero. It slopes downward when MP is negative.

Draw AP and MP on a separate graph

1. Keep labour on the horizontal axis.
2. Put product per unit on the vertical axis.
3. Plot AP and MP with clear labels.
4. Show MP reaching its peak before AP.
5. Show MP meeting AP at maximum AP.
6. Show MP touching the horizontal axis when TP is maximum.
7. Continue MP below the axis in Stage III.

Do not force AP to touch the horizontal axis merely because MP becomes zero. AP can remain positive even when MP is zero or negative.

What if Labour Does Not Rise One Unit at a Time?

The shortcut of subtracting consecutive TP values works only when the variable input rises by one unit.

Suppose a schedule is:

Workers	TP
0	0
2	20
4	52
6	72

From two workers to four workers:

Change in TP = 52 - 20 = 32
Change in L = 4 - 2 = 2

MP per additional worker = 32 / 2 = 16

Writing MP as 32 would treat the combined addition of two workers as the addition of one worker.

Reconstructing TP When MP Is Given

Because MP records successive additions to output, TP can be rebuilt by adding the MP values.

Suppose TP is zero at zero workers and the MP schedule is:

Worker	MP
1	8
2	12
3	15
4	11
5	4
6	0
7	-3

Add successively:

TP at 1 worker = 0 + 8 = 8
TP at 2 workers = 8 + 12 = 20
TP at 3 workers = 20 + 15 = 35
TP at 4 workers = 35 + 11 = 46
TP at 5 workers = 46 + 4 = 50
TP at 6 workers = 50 + 0 = 50
TP at 7 workers = 50 - 3 = 47

The reconstructed schedule is:

Workers	MP	TP	AP
1	8	8	8.00
2	12	20	10.00
3	15	35	11.67
4	11	46	11.50
5	4	50	10.00
6	0	50	8.33
7	-3	47	6.71

Maximum AP occurs at three workers in the listed schedule, so Stage I ends near that row. MP is zero at six workers, where TP reaches its maximum, so Stage II ends there. The seventh worker belongs to Stage III.

Reconstructing TP and MP When AP Is Given

If AP is given, first recover TP.

TP = AP by units of variable input

Suppose:

Workers	AP
1	6
2	8
3	9
4	8
5	7

Calculate TP:

At 1 worker, TP = 1 by 6 = 6
At 2 workers, TP = 2 by 8 = 16
At 3 workers, TP = 3 by 9 = 27
At 4 workers, TP = 4 by 8 = 32
At 5 workers, TP = 5 by 7 = 35

Now subtract consecutive TP values to obtain MP:

Workers	AP	TP	MP
0	-	0	-
1	6	6	6
2	8	16	10
3	9	27	11
4	8	32	5
5	7	35	3

This schedule has reached the end of Stage I around three workers, but it has not yet shown the end of Stage II. TP is still rising and MP is still positive at five workers.

Do not invent a zero or negative MP. State that the provided rows do not extend far enough to display Stage III.

Can You Identify All Three Stages From an Incomplete Schedule?

Not always.

If every MP value is positive and AP is still rising, the table only shows Stage I.

If AP has started falling but MP remains positive, the schedule has entered Stage II, but its right boundary is not yet visible.

If MP reaches zero but no negative value is shown, you can locate the end of Stage II, but Stage III itself has not yet appeared in the listed data.

If TP falls, Stage III is definitely present.

A precise answer describes what the evidence shows. It does not force all three stages into every table.

Common Mistakes and Their Repairs

Mistake	Why it goes wrong	Repair
Dividing TP by the previous labour value	AP uses the current input level	Use AP = current TP / current L
Dividing TP by labour to find MP	That gives AP	Find the change in TP and divide by the change in L
Saying TP falls when MP falls	MP may still be positive	TP falls only when MP is negative
Ending Stage I at maximum MP	Maximum MP marks the start of diminishing MP	End Stage I at maximum AP
Ending Stage II when AP begins to fall	That is the beginning of Stage II	End Stage II at maximum TP and zero MP
Treating zero MP as negative MP	Zero leaves TP unchanged	Negative MP makes TP fall
Writing AP as zero at zero labour	Division by zero is undefined	Use a dash
Rounding too early	Later comparisons can become misleading	Keep fractions or two decimal places until the final answer
Assuming every point in Stage II maximises profit	Product data alone do not show price or input cost	Call Stage II the relevant range, not one exact optimum

A Clean Answer Format for a Schedule Question

When asked to calculate the schedule and identify the stages, use this order:

1. Write the AP and MP formulas.
2. Complete the table carefully.
3. Show one sample AP calculation.
4. Show one sample MP calculation.
5. Mark maximum AP and the MP-AP crossover.
6. Mark maximum TP and zero MP.
7. Identify where MP becomes negative.
8. State the three stages with reasons.

Your conclusion can be compact:

That answer explains the boundaries instead of merely naming rows.

Quick Practice

Question 1

Find AP and MP.

Workers	TP
0	0
1	7
2	18
3	33
4	44
5	50
6	50
7	47

Question 2

If TP rises from 90 to 114 when labour rises from 6 units to 8 units, find MP per additional unit of labour.

Question 3

At a certain input level, AP is 14 and MP is 18. What will happen to AP after this additional unit is included?

Question 4

At a certain input level, TP is maximum. What is MP at that boundary?

Answers

For Question 1:

Workers	TP	MP	AP
0	0	-	-
1	7	7	7.00
2	18	11	9.00
3	33	15	11.00
4	44	11	11.00
5	50	6	10.00
6	50	0	8.33
7	47	-3	6.71

AP is highest around the third and fourth workers, with MP crossing AP in that region. Stage II ends at six workers, where TP is maximum and MP is zero. Stage III begins with the seventh worker.

For Question 2:

MP = (114 - 90) / (8 - 6)
   = 24 / 2
   = 12 units

For Question 3, AP rises because MP is greater than AP.

For Question 4, MP is zero.

The Final Memory Map

When time is short, remember four images:

• A bucket: TP is everything collected so far.
• A team average: AP is output per unit of variable input.
• The latest contribution: MP is what the newest unit adds.
• The fixed loom: early additions improve its use, later additions crowd it, and excessive additions create tangles.

Then remember the boundaries:

Maximum AP: Stage I ends
Maximum TP and zero MP: Stage II ends
Negative MP: Stage III begins

If you want to place this schedule inside the wider short-run and long-run story, read Returns to a Factor vs Returns to Scale.

Further Reading

• NCERT, Production and Costs
• SATHEE, Production and Costs
• MIT OpenCourseWare, Production and Cost Concepts
• OpenStax, Production in the Short Run

Frequently Asked Questions

What is the difference between TP, AP, and MP?

TP is the total output produced at a given input level. AP is output per unit of the variable input. MP is the extra output caused by an additional unit of that input.

How do I calculate AP from a TP schedule?

Divide TP by the corresponding number of units of the variable factor. If five workers produce 80 units, AP is 80 divided by 5, which equals 16.

How do I calculate MP when labour rises by one worker?

Subtract the previous TP from the current TP. If TP rises from 60 to 72, the latest worker’s MP is 12.

How do I calculate MP when labour rises by more than one unit?

Divide the change in TP by the change in labour. If TP rises by 30 while labour rises by 3 units, MP per additional unit is 10.

Why is AP undefined at zero labour?

AP equals TP divided by labour. Division by zero is undefined, so the zero-labour row should normally contain a dash for AP.

Can MP fall while TP is still rising?

Yes. TP continues to rise whenever MP is positive. If MP falls from 12 to 7, the latest unit still adds 7 units to TP, so TP rises by a smaller amount.

When does TP reach its maximum?

TP reaches its maximum when MP becomes zero. If MP turns negative after that, TP begins to fall.

When does AP reach its maximum?

In the usual smooth curves, AP reaches its maximum where MP equals AP. In a whole-number schedule, look for the highest AP and the point where MP crosses from above AP to below it.

Does Stage I end when MP is maximum?

No. Maximum MP marks the point after which marginal product begins to diminish. Stage I ends later, at maximum AP, where MP meets AP in the smooth-curve case.

Why is Stage II called the relevant stage of production?

In Stage I, the fixed factor remains relatively underused. In Stage III, extra variable input reduces total output. Stage II lies between those inefficient regions, although choosing an exact point within it requires price and cost information.

Can AP remain positive in Stage III?

Yes. AP measures the average output of all units employed, so it can remain positive even though the latest unit has negative MP and reduces TP.

Can every schedule show all three stages?

No. A schedule may stop while AP is rising or while MP is still positive. Identify only the stages supported by the given rows and do not invent missing values.